ScalingStacks

Proof. [0524]

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Proof.

Consider the case z≤−1z\leq-1. Since

(4.126) d​ζ−ζ−=d​r−r−+−1​J​d​r−r−=−h​d​z+ϵT−−1​J​h​d​z\frac{d\zeta_{-}}{\zeta_{-}}=\frac{dr_{-}}{r_{-}}+\sqrt{-1}J\frac{dr_{-}}{r_{-}}=-hdz+\epsilon_{T}-\sqrt{-1}Jhdz

The result then easily follows from the asymptotics of hh (4.16) and ω~\tilde{\omega} (3.349). ∎

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